Write the equation of the line passing through the points (-2,9) and (-9,2)

The solution to the system of equations y = -3x - 2 and 5x + 2y = 15 is (-19, 55).

In the given question, we have to find the solution to the system of equations y = -3x - 2 and 5x + 2y = 15.

The given equations are:

y = -3x - 2...................(1)

5x + 2y = 15...................(2)

Now solving the equation 2 by substituting the value of y from the equation 1.

5x + 2(-3x - 2) = 15

5x - 6x - 4 = 15

-x - 4 = 15

Add 4 on both side, we get

-x = 19

x = -19

Now putting the value of x in equation 1.

y = -3(-19) - 2

y = 57 - 2

y = 55

Hence, the solution to the system of equations y = -3x - 2 and 5x + 2y = 15 is (-19, 55).

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The complete question is:

What is the solution to the system of equations y = -3x - 2 and 5x + 2y = 15?

A circle is a closed two-dimensional shape because every point in the plane that makes up a circle is evenly separated from the "centre."

The collection of all points in the plane that make up a circle are all equally spaced from a certain point known as the "centre," making the form a closed two-dimensional shape. The reflection symmetry line is created by all lines that traverse the circle. Additionally, it is symmetrical in rotation around the centre at all angles.

The two foci are located in the middle of a circle, a particular type of ellipse.

a circle's equation, represented as (xh)2+(yk)2=r2, where r is the radius and (h,k) is the centre. The equation for the circle, which has a radius of 1, is x2+y2=1. Its centre is at the origin. x2+y2+cx+dy+e=0 is the formula for the equation of a circle.

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The future value of the $600 invested semi-annually at 8% nominal interest rate for 4 years is $1369.44 rounded to the nearest cent.

The formula to use in this case is FV = PV(1 + r/n)^nt, where FV is the future value, PV is the present value, r is the nominal interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

Given the information in the problem, we know that:

PV = $600 (the present value)

r = 0.08 (the nominal interest rate as a decimal)

n = 2 (the interest is compounded semi-annually)

t = 4 (the number of years)

Plugging these values into the formula, we get:

FV = $600(1 + 0.08/2)^(2*4)

To solve for FV, we need to calculate (1 + 0.08/2)^(2*4)

= (1.04)^8

=2.2824

FV = $600*2.2824

FV = $1369.44

Thus, the future value of the $600 invested semi-annually at 8% nominal interest rate for 4 years is $1369.44 rounded to the nearest cent.

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PV = $600 (the present value)

r = 0.08 (the nominal interest rate as a decimal)

n = 2 (the interest is compounded semi-annually)

t = 4 (the number of years)

Plugging these values into the formula, we get:

FV = $600(1 + 0.08/2)^(2*4)

To solve for FV, we need to calculate (1 + 0.08/2)^(2*4)

= (1.04)^8

=2.2824

FV = $600*2.2824

FV = $1369.44

For Trigonometric ratios, the values of sin, cos, and tan are defined by the ratio of sides of a right-angled triangle. The cosine of an acute angle in a right triangle is calculated using trigonometry.

By dividing the measurements of the side that it is adjacent to by the hypotenuse of the triangle.

The neighboring  base-to-hypotenuse ratio is known as the cos function. It aids in determining the triangle's side lengths regardless of the provided angle.

If the angle between the neighboring side and the hypotenuse of a right triangle is, we can write this using the cos function.

In a right-angled triangle, We calculate their values by the ratio

Cos = Base of the right-angled triangle/ Hypotenuse of the right-angled triangle.

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The unknown angle in the intersected line is as follows:

m∠ABD  = 46 degrees.

The lines intersected to form different angles. The angles are as follows:

m∠DBE = (8x - 7)°,

m∠DBC = (10x - 6)°

m∠EBC = 29°

The unknown angle ∠ABD can be found as follows:

∠ABC = 180(sum of angles on a straight line)

Therefore,

m∠DBC = m∠DBE +  m∠EBC

Hence,

10x - 6 = 8x - 7 + 29

10x - 8x = -7 + 6 + 29

2x = 28

x = 28 / 2

x = 14

Let's find the angle  m ∠ABD.

m∠DBC = 10x - 6 = 10(14) - 6 = 140 - 6 = 134 degrees

m∠ABD + m∠DBC = 180

m∠ABD  = 180 - 134

m∠ABD  = 46 degrees.

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Answer:

x = 65

y = 65

Step-by-step explanation:

This is a special right triangle with angle measures as follows:

90° - 45° - 45°

The side lengths are represented respectively as follows:

a√2 - a - a

The side length that sees angle measure 90°, hypotenus,   is given as 65√2.

The legs are congruent because this is a isosceles triangle at the same time so each = 65.

According to the equation, the weight of box in ounces is 64.

Firstly let us represent the weight of box with w. Now, the formula to be used for calculation of the weight of box is -

The weight of box in ounces = weight of box in pounds × number of ounces in one pound/one

Keeping the values in formula to find the value of weight of box in ounces.

The weight of box in ounces = 4 × 16/1

Performing multiplication and division on Right Hand Side of the equation to find the weight of box in ounces

The weight of box in ounces = 64 ounces

Thus, the weight of box in ounces is 64.

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The Mean of both the company is 2 while the variance of companies A and B is 0.6 and 1.6 respectively.

Here we have the probability distribution of both companies A and B

a)

We need to find the mean and variance of the companies.

Mean = E(X) = ∑xp(x)

Variance = E(X - Mean)²

Hence the mean of Company A will be

= [1 X 0.3] + [2 X 0.4] + [3 X 0.3]

= 0.3 + 0.8 + 0.9

= 2

Now Variance will be

0.3[1 - 2]² + 0.4[ 2 - 2]² + 0.3[3 - 2]²

= 0.3[1] + 0.4[0] + 0.3[1]

= 0.3 + 0.3

= 0.6

Now for Company B, we get mean to be

[0 X 0.2] + [1 X 0.1] + [2 X 0.3] + [3 X 0.3] + [4 X 0.1]

= 0 + 0.1 + + 0.6 + 0.9 + 0.4

= 2

The variance of Company B will be

0.2[0 - 2]² + 0.1[1 - 2]² + 0.3[2 - 2]² + 0.3[3 - 2]² + 0.1[4 - 2]²

= 0.2[4] + 0.1[1] + 0.3[0] + 0.3[1] + 0.1[4]

= 0.8 + 0.1 + 0 + 0.3 + 0.4

= 1.6

b)

Here we see that the value of the variance of company B is greater than A

Hence proved.

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Complete Question

Let the random variable X represent the number of automobiles that are used for official business purposes on any given workday. The probability distribution for company A

x         1         2         3

f(x)    0.3     0.4      0.3

and for company B

x         0         1         2         3         4

f(x)    0.2       0.1     0.3      0.3      0.1

a) Find the mean and variance of companies A and B

b) Show that the variance of the probability distribution of company B is greater than A

Answer:

396

Step-by-step explanation:

I found this answer by using standard multiplication but mentally.

4x9 is 36

and 4x9 is also 36, but for the sake of this way of solving we must add a zero the end of this answer making it 390

Now you have to add these two together:

    36

+ 360

  396

Hope this helps :)

Answer:

1. The total price you pay is $162.18

2. You earn $17,500

3. You earn $28.40

Step-by-step explanation:

1. 153 times 6% or 153 times 0.06 = 9.18

153 + 9.18 = 162.18

2. 350,000 times 5% or 350,000 times 0.05 = 17500

3. 710 times 4% or 710 times 0.04 = 28.4

Yes, the equation 9x^2 = 1 has zeroes at ±1/3. The solution is obtained by solving the algebraic equation.

What is algebraic equation?

The term "algebraic expression" refers to a mathematical expression that contains variables, constants, and algebraic operations (addition, subtraction, etc.). The expression must have an equals to sign in order to satisfy the algebraic equation.

We are given 9x^2 = 1

In order to find its roots, we need to find the value of x which are the zeroes for the equation.

So,

⇒9x^2 = 1

⇒x^2 = 1/9

⇒x = √1/9

⇒x = ±1/3

We are given 3x-1 = 0

So,

⇒ 3x = 1

⇒ x = 1/3

So, the given equation does not have its zeroes at ±1/3.

Hence, the equation 9x^2 = 1 has zeroes at ±1/3.

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The third part of the question is not complete as the complete equation is not visible.

A right triangle's hypotenuse is its longest side, its "opposite" side is the one that faces a certain angle, and its "adjacent" side is the one that faces the angle in question.

A right triangle's hypotenuse is always the side that faces away from the right angle. It is the right triangle's longest side. The adjacent and opposing sides are the other two sides. These sides have labels that relate to angles. From a particular angle, the other side is across.

The non-hypotenuse side next to a specific angle is referred to as the neighboring side. Sine, cosine, and tangent are three trigonometric functions that are defined by the terms hypotenuse, opposite, and adjacent.

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The complete question is:

What is the length of the side opposite the right angle?

One is a head of the other

To graphically solve a system of equations, we can plot the equations on a coordinate plane and find the point of intersection, which represents the solution to the system.

The first equation represents the total cost of the games, which is:

x(1.25) = 1.25x

The second equation represents the total cost of the rides, which is:

y(2.50) = 2.50y

The third equation represents the total cost of all games and rides, which is:

x(1.25) + y(2.50) = 12.50

We can also represent the fourth equation as the number of rides she went on is twice the number of games she played:

y = 2x

We can plot the first equation on the coordinate plane by treating x as the x-coordinate and 1.25x as the y-coordinate. We can plot the second equation in the same way, treating x as the x-coordinate and 2.5y as the y-coordinate.

We can plot the third equation as a line by treating x as the x-coordinate and 12.5-1.25x-2.5y as the y-coordinate.

Finally, we can plot the fourth equation as a line by treating x as the x-coordinate and 2x as the y-coordinate.

We can then find the point of intersection of the three lines, which represents the solution to the system of equations.

The point of intersection is the point (5,10) which means that Kaylee played 5 games and went on 10 rides.

The four basic algebra identities are as follows.

Algebraic expressions are mathematical expressions that result when we perform operations such as addition, subtraction, multiplication, and division on variables and constants. For example, let's say James and Natalie were playing with matches and wanted to create a pattern of numbers in matches. James played four games and formed No. 4. Natalie added three more games and two he formed a pattern of four. They realized they could add 3 matches to each round to get an extra '4'. From this, they concluded that, in general, 4 + 3 (n-1) double crochet stitches are required to create n 4 patterns. Here 4+ 3(n-1) is called an algebraic expression.

Algebraic identities are an important set of formulas in mathematics. They form the basis of algebra and help us perform calculations in simple and easy steps. Certain algebraic problems require a number of mathematical steps to be performed in order to arrive at an answer. Here, algebraic identities can be used to perform calculations without additional steps.

An algebraic identity is an algebraic equation in which the value of the left side of the equation is exactly equal to the value of the right side of the equation. The four basic algebra identities are as follows.

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The value of w has been solved to be 57.7 m.

Trigonometric functions are set of functions which can be applied so as to determine the unknown value of a side or angle of a right triangle. Some of the basic functions are: Sine, Cosine, Tangent etc.

In the given question, to solve for w let us applying sine function of the angle.

Sin θ = opposite/ hypotenuse

We have;

Sin θ = opposite/ hypotenuse

Sin 25 = 10/ w

w = 10/ sin 25

  = 57.6877

w = 57.7 m

The value of w is 57.5 m.

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The value of the equation is A = 21g + 3gh

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

A = g3 ( 7 + h )   be equation (1)

On simplifying the equation , we get

Applying the distributive property , we get

A = g3 ( 7 ) + g3 ( h )

A = 21g + 3gh

Therefore , the value of A is 21g + 3gh

Hence , the equation is A = 21g + 3gh

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It would take 4.0 minutes to paint the cone.

The original radius of the cone is √(49/π) inches

= √(49/3.14)

= √(15.7)

= 3.5 inches.

The new base area is 2 * 49π

= 98π square inches.

The new radius is √(98/π)

= √(98/3.14)

= √(31.4)

= 5.6 inches.

The new lateral surface area is π * 5.6 * 6

= 33.6 * π square inches.

The new total surface area is 33.6π + 98π

= 131.6π square inches.

Since it takes 1.5 minutes to paint the original cone, it would take

1.5 * (131.6/33.6) = 4.0 minutes to paint the new cone.

Hence, it would take 4.0 minutes to paint the cone.

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The nature of roots of the equation x² + 5x + 14 = 0 are of the form x = (-5 ± √(-31))/2, which are complex numbers and not real.

A quadratic equation is an equation of the form ax² + bx + c = 0, where a, b, and c are constants, and x is the variable. The nature of the roots of a quadratic equation can be determined by the discriminant, which is the value of b² - 4ac.

In this case, the quadratic equation is x² + 5x + 14 = 0. To find the nature of the roots, we need to find the discriminant, which is b² - 4ac:

Discriminant = 5² - 4 * 1 * 14 = 25 - 56 = -31

The discriminant can be used to determine the nature of the roots:

If the discriminant is greater than 0, the roots are real and distinct.

If the discriminant is equal to 0, the roots are real and identical (i.e., the equation has only one root).

If the discriminant is less than 0, the roots are complex and not real numbers.

In this case, the discriminant is negative, so the roots of the equation x² + 5x + 14 = 0 are complex. The roots can be found by factoring the equation into (x + a + bi)(x + a - bi), where a and b are real numbers, and i is the imaginary unit (i² = -1).

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Using the formula for angle of depression if the mirror is at a distance of 10.85 meters from the flagpole, then the height of the flagpole is 15.56 meters.

What is angle of depression?

An angle formed between a horizontal line and the line connecting an object and the observer's eye is referred to as the angle of depression. Two variables, namely height and distance, affect this angle.

The height of the school's flagpole = h

The distance from flagpole to mirror = 10.85 m

The distance from mirror to other side = 1.15 m

The height of Jevonte eyes' to the ground = 1.65 m

Let the angle of depression from Jevonte's point of view be represented by θ. Then apply the required trigonometric function -

tan θ = opposite / adjacent

tan θ = 1.65/1.15

tan θ = 1.4347

θ = tan^-1 (1.4347)

θ = 55.12°

For the given mirror, the angle of incidence is equal to that of reflection. Then apply the required trigonometric function -

tan θ = opposite / adjacent

tan 55.12° = h/10.85

1.4347 = h/10.85

h = 1.4347 × 10.85

h = 15.56

Therefore, the height value is obtained as 15.56 m.

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Susan will earn $24 of interest in 4 years.

Simple interest is the borrowing amount added only to the principal amount.

The formula to calculate the simple interest is;

                                                 S.I. = P x T x R / 100,

Where S.I. is simple interest, P is principal amount, T is time period and R is interest rate in a year.

Given:

Susan has $60 in a savings account.

The interest rate is 10% per year, and it's not compounded.

In 4 years,

     S.I. = P x T x R / 100

     S.I. = 60 x 4 x 10 / 100

     S.I. = $24

The earned amount in 4 years is $74.

Therefore, the earned amount in 4 years is $74.

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The value of the function ƒ(g(3)) is 239, when  ƒ(x) = x³ + 5x² − 2x − 1  and g(x) = x² – 4.

A function is an equation with just one solution for every value of y in the equation. A function pairs each input of a particular type with exactly one output.

Instead of y, it is typical to name functions f(x) or g(x). f(2) instructs us to calculate the value of our function when x is equal to 2.

We have given to find ƒ(g(3))

when ƒ(x) = x³ + 5x² − 2x − 1

and g(x) = x² – 4

When g(3) = (3)² – 4

= 9 - 4

= 5

For

ƒ(g(3)) = (5)³ + 5(5)² − 2(5) − 1

= 125 + 125 - 10 - 1

= 239

Thus, the value of the function ƒ(g(3)) is 239, when  ƒ(x) = x³ + 5x² − 2x − 1  and g(x) = x² – 4.

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The perimeter of the rug that has 110.5 square feet area is 43 ft

Area is the measure of the space occupied by a body bounded by an environment called perimeter, the same is expressed in units of squared side. Example: ft^2, m^2

To solve this geometry exercise the equation and procedure we will use is:

Where:

Information about the problem:

Clearing the width from the rectangle area formula, we get:

A = L * W

W = A / L

W = 110.5 ft^2 / 13 ft

W = 8.5 ft

With the width calculated we get the perimeter of the rectangular classroom:

P = (2*L) + (2*W)

P = (2*13 ft) + (2*8.5 ft)

P = 26 ft + 17 ft

P = 43 ft

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The equation for the inverse variation is:

d = 12/c

And evaluating that we can see that when c = 3, d = 4.

A genearl inverse variation equation can be written as:

y = k/x

Where k is a constant.

Here we know that there is an inverse variation between c and d, then we can write:

d = k/c

We know that d = 4/3 when c = 9, replacing that we will get:

4/3= k/9

9*(4/3) = k

12 = k

Then the equation is:

d = 12/c

Now we can evaluate this in c = 3 so we get:

d = 12/3

d = 4

When c =3, d = 4.

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A logarithmic function is increasing when the base, b of the function is greater than one i.e., b>1 , and the function is decreasing when the base b lies in the interval (0,1).

Logarithmic functions are inverses of exponential functions, and any exponential function can be expressed in logarithmic form. The form of the equation is y = log₂x. This can be read as "y is equal to the logarithm of x, base 2" or "y is equal to the logarithm of base 2, x". In exponential function form, x = 2ʸ.

The graph of logarithmic functions always passes through a point i.e., (1,0).

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The intersection of angle bisectors are equidistant from the sides of the triangle.

The intersection of all three of the triangle's interior angle bisectors is where a triangle's incenter is located. It can be thought of as the intersection of the triangle's internal angle bisectors.

What about angle bisectors is true ?

According to the angle bisector theorem, a point is equally distant from both sides of an angle if it is on the angle's bisector.

According to the converse of the angle bisector theorem, a point is on the angle's bisector if it is both in the interior of the angle and equally distant from its sides.

According to the given information

Angle bisector intersection points are evenly spaced from the triangle's sides.

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The equation, where p represents the jacket's original price, and the equation's solution is A. 1.08(0.8p - 5) = 46.44. The original price of the jacket was $60.00.

An equation is a mathematical statement showing that two mathematical expressions are equivalent or equal.

Equations are depicted using the equation symbol (=).

The total cost paid by Brian = $46.44

The discount on offer = 20%

Amount after the initial discount = 0.8p (1 - 20%)

Additional coupon = $5

Amount after the additional coupon = 0.8p - 5

Total discount = 20% + $5

Sales tax = 8%

Amount paid after the sales tax = (0.8p - 5)(1.08)

Original price = p

p = $60

1.08(0.8p - 5) = 46.44

1.08(0.8 x 60 - 5) = 46.44

1.08(43) = 46.44

46.44 = 46.44

Thus, Option A is correct.

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Answer:  g o f = {(2,2), (3,4), (4,3), (1,3)}

Step-by-step explanation: First we'll find f(x):-

f(1) = 2

f(3) =3

f(2) =4

f(4) =1

Now we'll find g(x):-

g(2) = 2

g(3) = 4

g(4) = 3

g(1) = 3

Therefore, gof(x) = {(2,2),(3,4),(4,3),(1,3)}

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(gof)(x) is a function that takes the input x and returns 3 if x = 1, 2, or 4, and 4 if x = 3.

To find the composite function (gof)(x), we first apply the function g to the input x, then apply the function f to the result.

For example, if we want to find (gof)(2), we first find g(2) = 2, then find f(2) = 4, so (gof)(2) = f(g(2)) = f(2) = 4.

So to find (gof)(x) we have to substitute the value of x in function g, then the output of function g in function f.

For the given set of functions f and g, the composite function (gof)(x) is:

(gof)(1) = f(g(1)) = f(3) = 3

(gof)(2) = f(g(2)) = f(2) = 4

(gof)(3) = f(g(3)) = f(4) = 3

(gof)(4) = f(g(4)) = f(3) = 3

So (gof)(x) is a function that takes the input x and returns 3 if x = 1, 2, or 4, and 4 if x = 3.

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